Rumors have been going around about an effort to reconcile the SSPX (Society of St. Pius X) with the Catholic Church.
Ed Peters has the canonical angle on the story and considers what scenarios might be possible that would allow a reconciliation, along with some commentary on how likely they respectively are.
I’d also add another scenario that strikes me as a possibility (at least hypothetically).
What we’re dealing with here is healing a schism, and the approach that has been taken in recent years in efforts to do that (i.e., in authentic ecumenism) has been to not worry about who was at fault in the past and instead make sure that we share those elements (or grow toward sharing those elements) that are needed for ecclesial communion.
Thus, for example, the joint declaration on Christology that was signed with the Assyrian Church of the East sidestepped the question of who was at fault back when the split occurred and instead said, in effect, "Look, regardless of what was said in the psat, we agree on this now, so this no longer a point that would bar us from ecclesial communion with each other."
A similar approach is used with the churches of the Reformation when it is possible to make common cause with them.
Since those in schism don’t like to admit that they’re in schism, this word also wouldn’t be used should we be able to reunite with the Assyrians. The Church would note the "separation" that existed historically between two groups but say that we now recognize that we share what is needed for full ecclesial communion, and so we’re announcing that fact.
(Forget being able to ever visibly reunite with any significant Protestant bodies–at least any time in this millennium. There’s just too much that’s not there at present.)
The thing that makes this "let’s not focus on the past" approach possible in a case like the Assyrian Church of the East or the Reformation churches is that the splits occurred so long ago that the original actors aren’t around any more.
That’s not the case with the SSPX. We’re talking about trying to heal this schism in its first generation, and that makes it a lot harder to take a "let’s not worry about who was at fault" approach.
Some version of this reasoning, though, could come into play if the SSPX schism is healed. It’ll certainly be a temptation since that’s the approach being used with others.
But it may not be prudent to proceed in that fashion with the SSPX.
A question that B16 should ask himself (and the SSPX bishops) is: "You guys disobeyed the direct orders of my predecessor in a grave matter pertaining to the structure of the Church, so what assurances do I have that you won’t do the same thing all over again?"
Only if B16 gets serious and credible assurances of fidelity should a face-saving method like the one mentioned above be considered.
I am not a scientist. I don’t even play one on TV.